It is imperative to transmit information without any loss in data communication. In a wireless communication system, however, a radio signal carrying information is distorted due to noises, multipath fading, interferences, and the like. Therefore, there have been many studies on error-correcting codes to improve signal reception reliability with the addition of well-controlled redundant information.
The polar code has been proposed first in 2008. The polar code is characterized by low coding and decoding complexity. The polar code is the first error correction code proved to be able to achieve the Shannon's channel capacity as a theoretical limit on the general Binary-input Discrete Memoryless symmetric Channel (B-DMC).
Meanwhile, the Successive Cancellation (SC) decoder proposed to decode the polar code has shown inferiority as compared to the Low-Density Parity Check (LDPC) code and Turbo code in SC decoding performance on the polar code having a finite code length N. Recently, a Successive Cancellation List (SCL) decoder has been proposed in order to overcome this performance inferiority.
The SCL decoder is an expanded SC decoder so as to decode the message bits successively through successive cancellation like the SC decoder. However, unlike the SC decoder having one decoding path, the SCL decoder has L decoding paths that are managed in a list and selects a codeword corresponding to one of L decoding paths. The codeword selection is performed under the rule of selecting the codeword having the highest posterior probability.
FIG. 1 is a graph illustrating a polar code decoding performance of an SCL decoder according to the related art.
Referring to FIG. 1, the horizontal axis denotes channel quality ((Eb/N0) and the vertical axis denotes the Bit-Error Rate (BER). FIG. 1 shows an error floor region 110 and a waterfall region 120.
Referring to FIG. 1, the decoding performance of the SCL decoder increases as the size L of the SCL decoder increases. As shown in FIG. 1, however, the decoding performance of the SCL decoder on the polar code having the finite code length N shows the error floor region 110. This is because the linear code generated according to the normal polar code generation method has a relatively short minimum distance.
FIG. 2 is a block diagram illustrating a configuration of a Cyclic Redundancy Check (CRC)-polar code concatenation encoder according to the related art.
Referring to FIG. 2, as one of the approaches to address the aforementioned issue of the SCL decoder, a method of concatenating a CRC code and a polar code has been proposed. A CRC-α coder 220 is a kind of error detection code. A message 210 is CRC-coded by the CRC-α coder 220 and polar-coded by a polar coder 230. Such coding operations are performed by a CRC-polar concatenation encoder 240.
FIG. 3 is a graph illustrating decoding performance of an encoder according to the related art.
Referring to FIG. 3, the horizontal axis denotes the channel quality (Eb/N0) and the vertical axis denotes the BER.
As shown in FIG. 3, the error floor region is overcome with the concatenation of the polar code and the CRC code.
The CRC code assists the SCL decoder to select a codeword corresponding to one of L decoding paths as the decoding results of the SCL decoder. The SCL decoder implemented by concatenating the CRC code with the polar coder removes the codewords that failed to pass the CRC test and selects the codeword having the highest probability among the codewords that passed the CRC test.
Therefore, a need exists for a method and an apparatus for efficiently encoding and decoding packets using a polar code.
The above information is presented as background information only to assist with an understanding of the present disclosure. No determination has been made, and no assertion is made, as to whether any of the above might be applicable as prior art with regard to the present disclosure.